Flip animation along an axis (Mirror animation)
Select all the bones involved in the animation of the right hand with your mouse over the graph editor press A to select all keyframes (make sure none are hidden), press W or right click and choose copy. 
Select all bones from the left hand, make sure they have an f-curve for the selected channels (i.e. insert one keyframe for each channel, loc, rot etc.), select a frame  where you can easily delete the new keyframes.
Go to frame 1 in your animation.
Pres RMB or W and choose paste flipped.